Under the Government's centrepiece Immigration Bill banks will have to check against a database of known immigration offenders before opening accounts.

Elsewhere, the bill will slash the number of grounds on which migrants can lodge an appeal, from the current 17 to just four - a move drawn up in response to the 12 years it took to deport radical cleric Abu Qatada.

Theresa May said: "We will be asking for a surcharge, there will be a sort of levy on people who are going to be coming here, to be staying for a while, to contribute so people can feel it is fair.

"One of the things the NHS has always been quite bad at is charging people who they should be charging, people who don't have the right to free access to the NHS and recovering those costs from them," she told BBC Breakfast.

And, as previously disclosed, a new requirement will be introduced for temporary migrants such as overseas students, to make a contribution to the National Health Service.

Immigration Minister Mark Harper said: "The Immigration Bill will stop migrants using public services to which they are not entitled, reduce the pull factors which encourage people to come to the UK and make it easier to remove people who should not be here.

"We will continue to welcome the brightest and best migrants who want to contribute to our economy and society and play by the rules. But the law must be on the side of people who respect it, not those who break it."

However Shami Chakrabarti, director of human rights group Liberty, said: "After the racist van stunt, the Home Office again scrapes the barrel by turning landlords into immigration officers and scrapping appeal rights for the vulnerable.

"Once more headline-grabbing gimmicks trump tackling departmental delays, and public fears are stoked instead of calmed by putting the house in order.

"Fair and legitimate immigration rules have their place but this nasty Bill is a race relations nightmare waiting to happen."